Counterfactual Potency

Transcription

1 Journal of Personality and Social Psychology 2010 American Psychological Association 2011, Vol. 100, No. 1, /10/$12.00 DOI: /a Counterfactual Potency John V. Petrocelli Wake Forest University Elise J. Percy and Steven J. Sherman Indiana University, Bloomington Zakary L. Tormala Stanford University Counterfactual thoughts typically take the form of implied or explicit if then statements. We propose that the multiplicative combination of if likelihood (the degree to which the antecedent condition of the counterfactual is perceived to be likely) and then likelihood (the perceived conditional likelihood of the outcome of the counterfactual, given the antecedent condition) determine the strength and impact of counterfactuals. This construct, termed counterfactual potency, is a reliable predictor of the degree of influence of counterfactual thinking upon judgments of regret, causation, and responsibility. Through 4 studies, we demonstrate the predictive power of this construct in a variety of contexts and show that it plays a causal role in determining the strength of the effects of counterfactual thought. Implications of counterfactual potency as a central factor of counterfactual influence are discussed. Keywords: counterfactual thinking, counterfactual potency, metacognition, regret, probability I came back thinking that I could have saved them all I should have saved them all but I couldn t... I was just a kid. Jose Ramos, Vietnam War veteran (quoted in McRoberts, 2003) Most tragic stories have one: a scene with a parent, police officer, friend, or war veteran who turns to a trusted confidant and describes all the things he or she could have done to avert an unwanted outcome. In the usual progression of such a scene, the listener often counters by insisting how implausible such a counterfactual world actually is. Sometimes, as in the case of the war veteran quoted above, these abstract questions of counterfactual plausibility can even cause tension within the self. These kinds of situations suggest that the perceived degree to which something could have been otherwise, and not only the sheer fact that something could have been otherwise, wields great influence in daily life. How can such a notion be conceptualized and quantified, and what might doing so reveal about how the alternative worlds that we construct affect our responses to reality? Counterfactual Thinking Since Kahneman and Tversky s (1982) seminal work on the simulation heuristic over 25 years ago, an enormous body of This article was published Online First November 29, John V. Petrocelli, Department of Psychology, Wake Forest University; Elise J. Percy and Steven J. Sherman, Department of Psychological and Brain Sciences, Indiana University, Bloomington; Zakary L. Tormala, Graduate School of Business, Stanford University. The contributions of the first and second authors were equal. We thank David Kenny for his insightful statistical feedback that facilitated the completion of this article. Correspondence concerning this article should be addressed to John V. Petrocelli, Department of Psychology, Wake Forest University, P.O. Box 7778, Winston-Salem, NC petrocjv@wfu.edu research has developed to illustrate the power of counterfactual thought over human judgment (for reviews see Mandel, Hilton, & Catellani, 2005; Roese, 1997; Roese & Olson, 1995b). Counterfactual thinking, as we treat it here, is characterized by conditional mutations of a past event (e.g., If only I hadn t taken out so many student loans, then I might be able to buy a house by now ; If she hadn t been wearing her seatbelt, then she could have been killed in that accident ). Such thoughts typically recruit alternatives that are better than the outcome that actually occurred (upward counterfactuals) rather than worse than the actual outcome (downward counterfactuals; see Markman, Gavanski, Sherman, & McMullen, 1993; Roese & Olson, 1997). Research on counterfactual thinking is particularly intriguing in that it turns the usual approach of judgment research on its head. That is, counterfactual research focuses not only upon psychological reactions to what actually did happen in a given instance but also upon reactions to what did not happen, and how notions of these other possible worlds influence judgments, feelings, and behaviors in response to the one world that truly exists (see Petrocelli & Sherman, 2010). Such thoughts have indeed been demonstrated as important factors in affect and judgment. For example, Wells and Gavanski (1989) demonstrated that ratings of an individual s causality for a tragedy increased when a salient counterfactual mutation of that individual s behavior would have averted the outcome (compared with a version in which such a mutation would not have changed the outcome), even though the actual behavior of the individual was the same in the two scenarios. However, the effects of counterfactual thought are not limited to the context of causal reasoning. Research has shown that counterfactual thoughts influence a wide variety of responses, including affective reactions (e.g., Johnson, 1986; Landman, 1987), feelings of satisfaction (e.g., Medvec, Madey, & Gilovich, 1995), judgments of blame and responsibility (e.g., Alicke, Buckingham, Zell, & Davis, 2008; Goldinger, Kleider, Azuma, & Beike, 2003; Miller & Gunasegaram, 1990), per- 30

2 COUNTERFACTUAL POTENCY 31 sonal feelings of regret (e.g., Miller & Taylor, 1995), and perceptions of regret experienced by other individuals (e.g., Kahneman & Miller, 1986; Kahneman & Tversky, 1982). This important role of counterfactual thinking is not a mere laboratory artifact or a phenomenon limited to scenario studies. On the contrary, particularly following undesirable events, such thoughts appear to be ubiquitous (see Hofstadter, 1979), spontaneous (Markman et al., 1993; McEleney & Byrne, 2006), and automatic (Goldinger et al., 2003; Roese, Sanna, & Galinsky, 2005). These thoughts naturally occur and influence real-life judgments, such as prisoners feelings of guilt for their crimes (Mandel & Dhami, 2005) or tendencies for self-blame among rape victims (Branscombe, Wohl, Owen, Alison, & N gbala, 2003). Further enhancing the power of counterfactual thoughts is the tendency for thoughts about what could have happened to become thoughts about what should have happened, a phenomenon known as the counterfactual fallacy (Miller & Turnbull, 1990). Counterfactual Potency In light of all this, the proposition that counterfactual thought influences affect and decision making is hardly a controversial one. However, the questions of when counterfactuals influence judgments, how strongly they influence judgments, and why particular counterfactual thoughts influence judgments more than others (i.e., what makes a particular counterfactual highly impactful) are issues that have only been investigated piecemeal. A consultation of most works describing circumstances that lead to influential counterfactual thought (e.g., Byrne, 2002; Kahneman & Miller, 1986; Roese & Olson, 1995a) will reveal the canonical form in which such findings are often presented: The List. That is, rather than a synthesis or explanation of what makes counterfactuals impactful, the existing literature delineates only the types of events associated with counterfactual thoughts. Counterfactual thoughts are likely or influential to the extent that they mutate an event that: was unexpected, was close to a desired outcome, involved an action rather than an inaction, was controllable, happened suddenly, and occurred early in a causal chain (see Byrne, 2002; Kahneman & Miller, 1986; Roese & Olson, 1995a). This list is a helpful and efficient way to distill information, explain findings, and make predictions. However, such a method of conceptualization is problematic in its theoretical clumsiness as well as in its lack of clear quantification and precise predictive value. To address these issues, we propose a single conceptual (and quantifiable) framework termed counterfactual potency and demonstrate its utility for furthering our understanding of the processes behind counterfactual thought. Such a conceptualization draws together what we believe are the two fundamental components of what makes counterfactual thoughts influential: the perceived likelihood of the antecedent in the counterfactual (termed if likelihood or IL) and the perceived conditional likelihood of the alternative outcome, given the antecedent condition (termed then likelihood or TL). The interactive effect of these two components constitutes counterfactual potency (CP), which we propose is a key predictor of the degree and strength of influence that a counterfactual thought (or set of thoughts) will exert. In addition to synthesizing much of what is known about counterfactual thinking, we believe that this approach provides a means of future innovation by raising new questions and generating novel predictions. We begin by drawing the evidence for the importance of IL and TL out of the existing literature individually, and then explain in more detail how they combine to form the construct of CP. We then describe a series of studies that demonstrate the ability of CP to explain and predict the influence of counterfactual thoughts on judgment. The Importance of If Likelihood (IL) In order for a counterfactual to be effective, one must believe that the proposed alternative antecedent condition (or the if part of the counterfactual) was reasonably likely, and the degree of this perceived likelihood should affect the influence of such a thought upon judgment. An alternative antecedent may consist of a different decision, a different behavior, or a different circumstance. The importance of perceived antecedent likelihood (IL) is buttressed by many lines of counterfactual research, including those on the simulation heuristic, expectancy violation, and counterfactual constraints, which we address in turn. The simulation heuristic (Kahneman & Tversky, 1982) is fundamentally linked to perceived likelihood. This is the phenomenon by which the effects of counterfactual thoughts are determined according to the ease of imagining them. In one seminal study, participants read about two men, Mr. Tees and Mr. Crane, both arriving late for a flight. In the scenario, Mr. Tees misses the flight by only 5 minutes while Mr. Crane misses it by 20. Despite their similar predicaments, participants expected Mr. Tees to be more disappointed with his outcome than Mr. Crane. A second study involving the story of Mr. Jones, a man who meets his untimely death in a traffic accident, showed that participants most commonly mutate deviations from routine behaviors (as opposed to routine behaviors themselves) in generating counterfactuals about tragic events. In both the case of the missed flight and the tragic automobile accident, results indicated the importance of the ease of imagining particular alternative antecedents, an indication of the perceived likelihood of the counterfactual. It is easier to imagine the means (i.e., alternative antecedent conditions) by which Mr. Tees could have avoided missing the flight than it is for Mr. Crane, and so Mr. Tees is expected to feel more disappointment. Likewise, it is easier to imagine behaviors (i.e., alternative antecedent conditions) that could have averted Mr. Jones s death that relate to deviations from routine (where high-likelihood alternatives are salient) than those that mutate normal events (where no such high-likelihood alternatives exist; see also Kahneman & Miller, 1986). Differences in the mutability of controllable versus uncontrollable events also have been conceptualized with an emphasis on a notion akin to antecedent plausibility (see Girotto, Legrenzi, & Rizzo, 1991; McCloy & Byrne, 2000). For example, Roese (1997) framed Markman et al. s (1993) finding (that gamblers tended to mutate the element of the game over which they perceived themselves to have control) in terms of research showing that people expect to have control over their lives (see Langer, 1975) and that differences in controllable versus uncontrollable elements in counterfactual thought may be seen as a special case of expectancyviolation effects. That is, the controllable event has a counterfactual antecedent with a higher a priori probability.

3 32 PETROCELLI, PERCY, SHERMAN, AND TORMALA To evaluate the evidence from the other angle, that of implausibility, it has repeatedly been shown that counterfactual thoughts usually avoid mutating antecedents for which alternatives are difficult to imagine. The relevant evidence indicates that people are more likely to mutate unstable rather than stable features of a situation (Girotto et al., 1991; Kahneman & Miller, 1986). Changes in stable factors are more difficult to imagine and thus are seen as less plausible than changes in unstable factors. Along the same lines, work on counterfactual constraints (mechanisms that preclude a class of events from mutation; see Seelau, Seelau, Wells, & Windschitl, 1995) such as natural-law constraints (e.g., laws of physics) has shown that antecedents for which alternatives are implausible (e.g., If only the laws of gravity were different... ) are generally not mutated in counterfactual thoughts (Rescher, 2001). In other words, influential counterfactual thought does not occur unless a plausible alternative antecedent is available. The Importance of Then Likelihood (TL) Despite the importance of antecedent plausibility (IL) in counterfactual thought, this characteristic is influential only to the extent that the change in the antecedent, however plausible or likely, is ultimately associated with an alternative outcome (TL). For example, only to the extent that Mr. Jones s deviation from routine is linked to avoidance of the undesirable outcome (e.g., If only Mr. Jones had taken a different route... vs. If only Mr. Jones had worn a different shirt... ) will mutations of that antecedent exert effects upon judgment, regardless of how plausible the alternative antecedent is perceived to have been. For that reason, the influence of perceived antecedent likelihood is always contextualized by the associated antecedent alternative outcome contingency (TL). Prior research has established that the ability of a counterfactual to undo an outcome is an integral factor in its effectiveness. Take, for example, Wells and Gavanski s (1989) finding that the influence of a salient alternative antecedent depends on its association with a change in the outcome. In their research, attributing the cause of a tragedy to a particular individual (an employer who ordered an allergenic dish for his employee at a restaurant, resulting in her death) was dependent upon the contingency between the alternative antecedent condition (a different dish choice) and an alternative outcome (successful avoidance of the allergic reaction). Participants who read a version in which both dishes would have contained the lethal allergen assigned less causality to the employer for the tragedy than did participants who read a version in which the alternative dish would have been safe for the employee to eat. Additional evidence for the importance of TL comes from research by Branscombe, Owen, Garstka, and Coleman (1996). They demonstrated that blame to victims versus perpetrators in a rape scenario depended on whether a change to that target s behavior would have changed the outcome. In models of counterfactual-based causal reasoning (see Spellman, 1997; Spellman, Kincannon, & Stose, 2005; Walsh & Byrne, 2004), an integral component of causality judgments is the perception of the strength of the antecedent outcome relationship. Only to the extent that changes to the antecedent are perceived to be related to changes in the outcome will counterfactuals about a particular change in an antecedent (selected from infinite possible antecedents) lead to a perception that the antecedent plays a causal role (see Hart & Honoré, 1985). In other words, when using counterfactuals to reason about causation, something akin to TL is of prime importance. The importance of such antecedent outcome contingencies is also supported by work on semifactuals (Barker, 1991; Goodman, 1973), or even if thoughts (see Green, Applebaum, & Tong, 2006; McCloy, & Byrne, 2002). These thoughts alter an antecedent without altering the outcome (e.g., Even if I had studied harder, I still might have failed chemistry ). Neither IL nor TL operates independently, but rather each component contextualizes the other s effect. For example, despite the fact that perceptions of antecedent outcome contingencies are important in causal reasoning about counterfactuals (Hilton, 1988; Mandel, 2003; Spellman, 1997), the cognitive availability of alternative antecedents has been shown to moderate this influence. Specifically, explicit references to changes in particular antecedents can change perceptions of causation, even if contingencies are held constant (see Byrne & McEleney, 2000). Such research (and the evidence for the overall importance of IL described earlier) supports the important relationship between the two components, such that the ultimate influence of a counterfactual thought is determined by their interaction. We now describe in more detail the combination of these factors into CP. Counterfactual Potency: Integrating IL and TL In this article, we propose counterfactual potency (CP) as a new manner of conceptualizing the influence of counterfactual thought. Along with this proposal, we formulate and test a quantitative approach for using CP to predict the influence that any particular counterfactual thought (or set of thoughts) will have upon subsequent affect and judgment. Notably, this proposal does not constitute a challenge to existing theory or research. As should be clear from the discussion above, the individual notions of IL and TL emerge directly from existing work on counterfactual thought, and our thinking owes greatly to Roese and Olson s (1995a) discussion of antecedent-based and outcome-based determinants of counterfactual thought, as well as Kahneman and Tversky s (1982) important work on the simulation heuristic. Our conceptualization also derives partly from previous work on counterfactual thinking and judgments of causality, particularly the work of Gleicher et al. (1990) and Spellman et al. (2005). Spellman and colleagues theorized that people can estimate the probability of an alternative outcome (e.g., the probability that a tragedy could have been avoided) by first considering all of the ways that an event could have unfolded (i.e., the various alternative antecedents). The probability of an alternative is then obtained by summing each of the products of the probabilities of the ways that could have occurred and their conditional probabilities (i.e., probabilities of an alternative outcome given that the way occurred). Our primary proposition is that the effect of any particular counterfactual on judgment is a function of the interaction between two independent probability judgments: the perceived a priori likelihood of the antecedent condition (IL) and the perceived likelihood of the alternative outcome given the antecedent condition (TL). We propose that the interactive relationship between these two components (CP) can explain many circumstances known to make one counterfactual more or less impactful (or more

4 COUNTERFACTUAL POTENCY 33 or less likely to be spontaneously generated) than another. This construct, both quantifiable and measurable, is a promising means of predicting and understanding the effects of counterfactual thought. We propose that the influence of any counterfactual can be accurately predicted by the interaction of IL and TL (each of which exists on an independent continuum ranging from very low to very high perceived likelihood). In other words, a counterfactual should exert influence to the extent that both the alternative antecedent is plausible and that such a change to the antecedent would be associated with an alternative outcome of interest. Our approach is distinct from that of Spellman et al. (2005) in at least a few important ways. First, our approach constitutes a methodological advance, in that it involves measuring CP for individual counterfactuals via IL and TL ratings, and thereby provides a measure that can be employed to predict the effects of a single counterfactual thought or set of thoughts. Spellman et al., on the other hand, provided a more general theory for how the probability of an alternative event (and thus causation) is assessed. Second, CP constitutes a theoretical advance in that it broadens the scope of probability judgments in this domain beyond causation to explain and synthesize a very wide range of counterfactual thinking phenomena. Finally, our approach extends Spellman et al. s theorizing about how people assess probability to determine causation by examining how multiple probability judgments interact to determine the influence of counterfactuals. IL and TL Are Independent and Subjectively Determined IL and TL (although they may be correlated under certain circumstances) are theoretically independent. Indeed, imagine the (implausible) counterfactuals that could be generated by a person watching coverage of a plane crash on the evening news. It is possible, within a particular counterfactual, for IL to be very low while TL is very high (e.g., If only aliens had intervened, then the plane might not have crashed ). On the other hand, TL may be low while IL is high (e.g., If only I had used my usual toothbrush today, then the plane might not have crashed ). In short, the perceived a priori likelihood of the antecedent condition in a counterfactual is not dependent upon the contingency between the antecedent and the alternative outcome or vice versa. Also important, IL and TL are subjectively determined; it is the perceived likelihoods that are important for the purposes of CP, not the objective or true likelihoods. If, for example, one really believes that the use of a particular toothbrush would have averted the disasters of the world (or, alternatively, that the intervention of aliens is plausible), such counterfactuals as described above may truly be impactful upon that person s affect and judgments. One direct result of this subjective quality is that CP is not dependent upon the particular content of any given counterfactual per se two different people could generate the same counterfactual and have very different levels of CP. Counterfactual Potency as a Metacognitive Construct By definition, IL and TL are metacognitive constructs in that they constitute judgments or thoughts about one s own (counterfactual) thoughts. As such, the CP construct owes to previous research demonstrating that judgments about one s own thoughts (be it judgments of accessibility, fluency, or confidence) in part determine the effects of such thoughts on subsequent judgment and behavior (see Petty, Briñol, Tormala, & Wegener, 2007; Schwarz et al., 1991; Schwarz, Sanna, Skurnik, & Yoon, 2007; Schwarz & Vaughn, 2002; Tversky & Kahneman, 1973). It is important to note that, like other metacognitive phenomena, the processes involved need not be explicit or deliberative to wield influence (see Reder & Schunn, 1996). We do not submit that decision makers consciously and deliberately measure and combine IL and TL in order to make judgments subsequent to counterfactual thought. However, we do believe that CP as we define and measure it captures the essence or substance of what makes a counterfactual thought seem plausible, and thereby influential. Within the broader literature on metacognition, one particularly relevant framework for CP is that of thought confidence, developed by Petty, Briñol, and Tormala (2002; see also Briñol & Petty, 2009). This work has shown that confidence in one s own thoughts is an important variable in persuasion and resistance processes. In particular, thought confidence has been shown to moderate the impact of thoughts on attitudes, such that thoughts are impactful upon attitudes only to the extent that they are associated with some degree of confidence. Although CP is conceptualized, measured, and employed in a manner quite different from the construct of thought confidence, it is analogous to this construct in that it constitutes a metacognitive sense of confidence or degree of belief in one s thoughts that can be used to predict the influence of those thoughts on later judgment. The Measurement of CP To measure CP, we have adopted the general paradigm of having participants supply counterfactuals and subsequently rate each of those counterfactuals for both IL (i.e., Look at the if part of your statement. What was the likelihood of that actually happening? ) and TL (i.e., Now look at the then part of the statement you supplied. Given that the if part had taken place, what do you think was the likelihood of that actually happening? ) for each counterfactual generated on corresponding response scales (e.g., ranging from not at all likely [1] to highly likely [9]). We then use these data to predict the effects of those thoughts upon subsequent affect and judgments. We have also manipulated IL and TL in experimental paradigms to assess the role of these factors in determining the impact of counterfactual thoughts. We propose here (and offer empirical support of the notion) that such measures of IL and TL combine multiplicatively within a given counterfactual to produce CP (i.e., IL TL CP). 1 With such an approach, counterfactuals for which IL and TL are both high should exert particularly strong effects on affect and judgment, whereas counterfactuals for which either component is low should exert a weak effect. In other words, any situation in which one or both components are very low will lead to a relatively impotent counterfactual (i.e., multiplying 100 by zero, similar to multiplying zero by zero, produces zero). However, it is important 1 Such a multiplicative term is analogous to other theoretical interactions, such as McGuire s (1968) notion of the interactive relationship between reception and yielding in persuasion.

5 34 PETROCELLI, PERCY, SHERMAN, AND TORMALA to note that, in order to control for the potential lack of scale invariance across the measures of the two components, the independent effects of IL and TL must be considered when CP is computed. In other words, in addition to their interactive effect, it is possible for IL and TL to exert main effects, and these must be partialed out to interpret the interaction. In some cases, without controlling for the component effects, the apparent correlation (or lack thereof) between CP and other measures could be misleading. For this reason, we do not advocate merely computing CP and investigating its correlation with other measures IL and TL must be independently considered as well. In addition to being a characteristic of individual counterfactuals, to the extent that a set of counterfactuals mutates behavior of a particular target toward a particular end (e.g., If only I had studied harder for the test I might have passed, If only I hadn t partied so much the night before the test I might have passed, etc.), one should be able to assess CP across multiple counterfactuals using an averaging method. 2 In this way, CP can be measured across multiple counterfactuals and used to predict postcounterfactual judgments and affect. Overview of Studies As a means of clarifying and testing our proposed construct of CP, we conducted four studies. Study 1 demonstrated that CP is a reliable predictor of the relationship between counterfactual thought and judgment in a correlational design; this study also showed the predictive ability of CP when averaged across multiple counterfactuals. In Study 2, we assessed the causal role of the IL TL interaction by manipulating IL and TL for a salient counterfactual about an event. Study 3 demonstrated the effects of manipulating judgments of an event through feedback about counterfactual likelihood and showed that CP mediates and explains these effects. Study 4 investigated the predictive power of CP for judgments about a personally involving decision, in which we manipulated IL and TL in a gambling task and showed that CP explains judgments both when the alternative outcome is known and when it is not. Study 1: Mr. Jones : The Predictive Power of CP The purpose of Study 1 was twofold. First, we set out to demonstrate how IL and TL could be successfully measured as distinct components of counterfactual thoughts. More important, we examined whether our measure of CP (the multiplicative combination of IL and TL) was a reliable predictor of the influence of counterfactual thinking on judgments. In doing so, we used a modified version of a classic scenario from early counterfactual research (that of Mr. Jones from Kahneman & Tversky, 1982) and measured participants estimates of IL and TL for each if only statement generated. We also manipulated the frequency of counterfactual thoughts (by asking participants to list one, three, or five counterfactual thoughts) so that we could examine the predictive power of CP both in the case of a single counterfactual as well as when averaged across multiple counterfactuals. Additionally, such a manipulation allowed us to compare the predictive ability of CP to that of sheer counterfactual frequency. Method Participants and design. A total of 92 undergraduate students, enrolled in an introductory psychology course at Wake Forest University, took part in the study in exchange for partial course credit. The data of two participants were excluded from analysis due to responding to several items well above or below 3 SDs from the means, reducing the total sample to 90 participants. We employed a 3 (counterfactual thought frequency: one, three, or five) 2 (order of IL/TL measurement: before vs. after other dependent variables) between-participants factorial design. Procedure. Upon arrival, participants were greeted by a laboratory assistant who presented a brief, oral introduction to the experiment described as a study of social perception. Participants were escorted to a cubicle equipped with a personal computer. Experimental materials were presented using MediaLab v2006 Research Software (Jarvis, 2006). The instructions of the experiment were self-paced, and participants advanced the instructions by pressing a response key. Event. Participants were presented with a modified version of a scenario used by Kahneman and Tversky (1982), which described the tragic automobile accident of Mr. Jones. The scenario described several features that potentially could be mutated: (a) driving his wife s car to work (because he forgot to fill up his truck with gas); (b) leaving work earlier than usual to attend to some long-overdue household chores that he promised his wife he would complete; (c) using a rarely used route along the shore to enjoy the view; (d) stopping along the way to buy an ice cream; (e) listening to the radio full-blast; and (f) braking hard while crossing an intersection. Mr. Jones was described as suffering severe injuries and being confined to a wheel chair following the accident. Thought-listing task. After reading about the event, participants read that, as commonly happens in such situations, Mr. Jones often thought and often said, If only..., then this terrible accident might have been avoided, during the days that followed the accident. Participants were asked to list either one, three, or five ways in which Mr. Jones might have completed this thought. They were instructed to begin each thought with the words If only Mr. Jones... and to complete it with then this terrible accident might have been avoided. Counterfactual potency. Participants were randomly assigned to one of two order conditions, whereby they responded to the IL and TL items either before or after the measurement of the other dependent variables. To complete these measures, each counterfactual that had been generated was presented back to the participant one at a time. To measure IL, participants were asked to consider just the first part of the thought (i.e., the if part of the statement) and to report their perceived likelihood of Mr. Jones actually doing that using a 9-point scale anchored at extremely unlikely (1) and extremely likely (9). To measure TL, participants were asked to consider just the second part of the thought (i.e., 2 Although other models for combining CPs for multiple counterfactuals were considered (e.g., an additive model), our comparisons of the available methods have shown that an averaging model leads to the strongest predictive power. Although we feel that the simultaneous predictive ability and elegance of an averaging model serves our purposes here, the question of whether more complex models may provide even stronger predictive power is a reasonable one that deserves future attention.

6 COUNTERFACTUAL POTENCY 35 the then part of the statement) and to indicate the likelihood of the accident having been avoided, given that Mr. Jones had done the behavior in the if part (using the same 9-point scale). The process of providing IL and TL ratings was repeated for each counterfactual that a participant generated (e.g., a participant who generated three counterfactuals would go through the IL/TL rating process a total of three times). Dependent variables. Participants were asked to respond to eight different dependent variable items, including how responsible Mr. Jones was for the accident; how much Mr. Jones was to blame; how careless he was; how foolish he was; how much regret, bitterness, and disgust they thought Mr. Jones feels with regard to the accident; and how much they thought Mr. Jones blames himself for the accident. Participants responded to each of the items using a 9-point response scale with very little (1) and very much (9) as the anchor labels. Results and Discussion Preliminary analyses. To simplify the report of our findings, we first subjected the eight dependent variables to a principal components factor analysis with oblimin rotation to assess how they might best be combined. This preliminary analysis indicated that the two items that implicated Mr. Jones as responsible and blameworthy for the accident loaded on the first factor, whereas the other six items loaded on the second factor of a two-factor solution. These two factors, which we term Responsibility/Blame and Negative Affect, explained 56.48% of the variance in the data. Further, the responsibility and blame items had a Cronbach s alpha of.80, and the other six items had a Cronbach s alpha of.76. Counterfactual potency. To compute CP, we first multiplied each individual IL/TL pair to yield CP for each counterfactual and then averaged these products for the participants who generated more than one. For participants who generated only one counterfactual, the CP value for that counterfactual was used. This variable thus represents the average CP estimate for each participant s counterfactual thoughts. To investigate whether thought frequency or task order had any unintended influence upon the IL and TL measures, we subjected CP to a 3 (counterfactual thought frequency: one, three, or five) 2 (order of IL/TL measurement: before vs. after other dependent variables) analysis of variance (ANOVA). This analysis revealed an unanticipated main effect for thought frequency, F(2, 84) 6.98, p.01. Participants who were asked to list a single counterfactual thought reported a significantly smaller CP estimate (M 23.00, SD 9.74) than did participants who were asked to list three counterfactuals (M 31.86, SD 11.60), t(84) 3.33, p.01, or five counterfactuals (M 31.40, SD 8.70), t(84) 3.14, p Participants who were asked to list three counterfactuals did not report a significantly different CP estimate from participants asked to list five, t(84) 0.17, ns. No effects involving the order manipulation were observed (Fs 1). Dependent variables. Preliminary analyses revealed no significant effects involving the order manipulation. Thus, order of measurement is not discussed further. As a formal test of our hypotheses, the analyses of primary interest concerned whether CP was a reliable predictor of the dependent variables when each of its individual components (IL and TL) was taken into account. We were also interested in whether CP would be a more reliable predictor than simple counterfactual thought frequency. To this end, we computed hierarchical regression models, entering counterfactual thought frequency, IL, and TL in the first step and CP (i.e., IL TL) in the second step. 4 For the model predicting responsibility/blame, number of counterfactual thoughts was marginally related to judgments (.19), t(86) 1.75, p.08; a marginal effect was found for IL (.18), t(86) 1.63, p.11; and a significant effect was found for TL (.29), t(86) 2.85, p.01. The second step of the analysis showed that, controlling for these other influences, the CP estimate significantly accounted for variance in responsibility/ blame attributed to Mr. Jones for the accident (.29), t(85) 2.02, p.05. Similar results were found for the model predicting negative affect. Although the data did not reveal a main effect of counterfactual thought frequency (.04), t(86) 0.32, ns, significant main effects were found for IL (.26), t(86) 2.31, p.05, and TL (.23), t(86) 2.23, p.05. Again, though, the second step of the analysis showed that the CP estimate significantly accounted for variance in negative affect judgments above and beyond the other predictors (.31), t(85) 2.11, p.05. In short, the more that participants simultaneously felt that (a) an alternative behavior on the part of Mr. Jones was possible and that (b) such an alternative behavior would have led to a different and more desirable outcome, the more responsibility/blame they assigned to Mr. Jones and the more negative affect they expected him to experience. In addition to demonstrating how CP (the multiplicative product of IL and TL) can be measured and used to 3 These findings are contrary to what one might expect, given that an observer s first counterfactual thought might be expected to be more salient and, thus, more potent than subsequent counterfactuals. However, participants were cognizant of the number of thoughts they were being asked to list before they began listing their thoughts. We suspect that requesting multiple counterfactual thoughts, as opposed to only one, enhanced the salience and perceived relevance of counterfactual thinking in response to the scenario. This ultimately may have made it seem that any single alternative antecedent was actually more likely to occur and subsequently inflated CP estimates in the three and five-thought conditions. 4 Providing a basic demonstration that our construct generally predicts postcounterfactual judgments, across conditions CP was found to be significantly correlated with both responsibility/blame (r.25, p.02) and negative affect (r.36, p.001). We also examined the correlations between CP and the dependent variables in each of the three conditions separately. All of the correlations for the three- and five-counterfactual conditions were statistically significant (all rs.35, all ps.05). However, for the one-counterfactual condition, the relationship between CP and responsibility/blame failed to reach significance (r.17, ns), and the CP negative affect correlation reached only marginal significance (r.33, p.07). These results likely stem from the fact that we observed less variance in our measure of CP when it was derived from a single counterfactual thought. Although we find these correlations to be informative in this initial test, we caution against interpreting the correlation between the IL TL product and some criterion without partialing out the component variables (see our discussion regarding scale invariance across the measures of the two components in the section The Measurement of CP). We include the correlations here (drawn from IL and TL measures that were conceptually scales from 0% probability to 100% probability, and thus arguably scale invariant) only to make the relationships between all study variables clearer to our audience.

7 36 PETROCELLI, PERCY, SHERMAN, AND TORMALA predict judgments, results of Study 1 also suggest that CP offers more predictive utility than the sheer frequency of counterfactual thoughts generated (a characteristic that to this point has been the only quantitative index used to predict counterfactual thought effects; see Roese, 1997; Seta, Seta, McElroy, & Hatz, 2008). Results also clarified that both CP for a single counterfactual as well as an average CP (in the case of multiple counterfactuals) can predict judgments. Study 2: Let s Make a Deal: Manipulation of IL and TL Whereas Study 1 demonstrated the predictive power of CP in a correlational design, we devised Study 2 to demonstrate the causal role of the IL TL interaction in judgment. To do so, we created a paradigm that made a particular counterfactual salient while independently manipulating that counterfactual s associated IL and TL. To accomplish this, we had participants learn about a contestant s experience on a game show (loosely based upon the Let s Make a Deal game show that originally aired in the 1960s), in which, after choosing the wrong game show door, the contestant loses. Four versions of the game s events were constructed to directly manipulate IL and TL for the salient counterfactual. After reading the scenario, we assessed IL, TL, and judgments about the event (negative affect and responsibility). The predicted causal role of the IL TL interaction would be demonstrated by a two-way IL Condition (low, high) TL Condition (low, high) interaction upon the dependent measures. Moreover, we predicted that participants own judgments of CP (the interaction of the IL and TL ratings for the salient counterfactual) would have predictive value. Method Participants and design. A total of 153 undergraduates, enrolled in an introductory psychology course at Wake Forest University, participated in exchange for partial course credit. The data of two participants were excluded from the analyses due to one participant s failure to complete the protocol and another participant s CP score being greater than 4 SDs above the mean. Thus, the final sample consisted of 151 participants. The current study employed a 2 (IL condition: high vs. low) 2 (TL condition: high vs. low) 2 (order of measurement of IL/TL: before vs. after other dependent variables) between-participants factorial design. Procedure. All of the basic procedures and experimental materials were presented in the same way as in Study 1. Again, the experiment was described as a study of social perception. Scenario. Participants were presented with a scenario involving a modified version of the TV game show Let s Make a Deal. The target in the scenario was a 35-year-old auto mechanic named Sam. Participants read the following: One day Sam is on the game show Let s Make a Deal. Sam s options include picking Door #1, Door #2, or Door #3. Behind two of the doors there is nothing. Behind one of the doors is a man who will ask him a trivia question. If Sam picks the correct door, and subsequently answers the trivia question correctly, he will win $50,000. Otherwise, Sam will get nothing. Thus, Sam has to do both things in order to win: pick the correct door and correctly answer the question asked by the person behind the door. In order to manipulate the IL and TL for the salient counterfactual ( If only Sam had picked Door #2, then he might have won ), we varied certain characteristics of the event. First, participants were randomly assigned to one of two IL conditions. In the low IL condition, Sam was depicted as having been very unlikely to have picked Door #2, the correct door. In this condition, participants read the following: Sam wastes no time at all in selecting a door. His favorite number is 3. Like his favorite baseball player, Babe Ruth, Sam s softball jersey number is 3. No doubt, Sam picks Door #3. In the high IL condition, Sam was depicted as having very nearly chosen Door #2. In this condition, participants read the following: Sam takes his time in selecting a door. He agonizes over the decision. Sam thinks about Door #2 as well as Door #3. He goes back and forth in his mind. The game show host pressures Sam for an answer. At the last moment, Sam picks Door #3. All participants then read that the game show host opened Door #3, and with a disappointed sigh from the audience, nothing was found behind the door. Participants were informed that the person posing the trivia question was actually behind Door #2. The game show host then said, Well, let s at least see the category that the trivia question was from, behind Door #2! The category of the question Sam would have been asked: Ancient Aztecs. Participants were also randomly assigned to one of two TL conditions. Participants in the low TL condition read that, after the category of the question was announced, Sam commented: I know very little about the Ancient Aztecs. Thus, participants were led to believe that, even if Sam had chosen the correct door, ultimately winning the prize would remain unlikely. Participants in the high TL condition read that, after the category of the question was announced, Sam s eyes grew large, and he commented: I just watched, on television, an in-depth documentary about the lives of the Ancient Aztecs! In this case, participants were led to believe that, if Sam had chosen the correct door, there was a high likelihood that he would have won the prize. Counterfactual potency. Participants were asked to respond to two items similar to those used in Study 1. We did this partly to determine whether the IL and TL manipulations were successful, but more importantly so that we could examine the ability of their multiplicative combination (CP) to predict their judgments. As in Study 1, participants were randomly assigned to one of two order conditions, such that they responded to these items either before or after the measurement of the other dependent variables. Because participants were not asked to list their thoughts (but rather responded with reference to a particular counterfactual), we provided detailed instructions to ensure that participants were clear about what we were asking them. Participants read the following: You might be thinking: If only Sam had picked Door #2, then he might have won the money. This is an example of an if then statement. People often make if... then statements after undesirable outcomes that are nearly desirable. For example, imagine a doctor who has to decide upon one of two treatments for a patient with a serious disease. The doctor decides on Treatment A and, unfortunately, the patient dies. The doctor might say, IF only I had chosen

8 COUNTERFACTUAL POTENCY 37 Treatment B, THEN the patient might have lived. We might ask the doctor questions about this if... then statement: 1) Consider the IF part of that statement: At the time you decided, how likely were you to choose Treatment B instead of Treatment A? (i.e., how close did you come to choosing Treatment B instead of Treatment A?); and 2) Consider the THEN part of that statement: Assuming you had actually chosen Treatment B instead of Treatment A, then how likely do you think it was that the patient would have lived? Make sure you understand the difference between these two kinds of questions before moving on to the next screen frame. Following these instructions, to measure IL, participants were asked, If only Sam had picked Door #2, then he might have won the money. Consider just the first part of this thought. What do you perceive was the likelihood of Sam actually picking Door #2? To measure TL, we asked, If only Sam had picked Door #2, then he might have won the money. Consider the second part of this thought. That is, given that Sam had picked Door #2, what do you perceive was the likelihood that he would have correctly answered the question? Participants responded to both questions on a 9-point scale anchored at extremely unlikely (1) and extremely likely (9). Dependent variables. Following the measures of IL and TL, participants were asked to respond to eight different dependent measures, assessing how responsible Sam was for the outcome, how much Sam was to blame, as well as how much anger, regret, bitterness, sadness, disappointment, and disgust Sam felt with regard to the outcome. Participants responded to each of the items using a 9-point scale anchored at very little (1) and very much (9). Results and Discussion Preliminary analyses. Similar to Study 1, we subjected the eight dependent variables to a principal components factor analysis with oblimin rotation in order to identify how the variables might best be combined. This preliminary analysis revealed a factor structure similar to that found in Study 1. The two items that implicated Sam as responsible and blameworthy for the outcome loaded on the first factor (referred to as Responsibility/Blame), whereas the other six items loaded on the second factor (referred to as Sam s Negative Affect) of a two-factor solution. These two factors explained 70.42% of the variance in the data. Furthermore, the responsibility and blame items had a Cronbach s alpha of.77, and the negative affect items had a Cronbach s alpha of.91. Dependent variables. As in Study 1, no significant effects involving the order of the measures were obtained, so we do not discuss this issue further. In a more precise test of our hypotheses, we expected to find interactions between manipulated IL and TL for our dependent variables, such that negative affect and judgments of responsibility/blame would be greatest when both IL and TL were high. When either or both are low, the salient counterfactual ought to have little impact. Moreover, we expected that IL and TL ratings would explain this effect. To test this hypothesis in a context in which mediation analysis was not ideal, 5 we conducted a conceptually similar analysis by demonstrating three relationships: (a) the IL/TL manipulations influenced the dependent measures in the predicted interactive fashion (i.e., the manipulation 3 dependent measure relationship); (b) the IL and TL manipulations influenced IL and TL ratings as predicted (i.e., the manipulation 3 mediator relationship, synonymous for our purposes with a manipulation check); and (c) IL and TL ratings have the predicted interactive effect upon the dependent measures (the mediator 3 dependent measure relationship). Responsibility/blame. To assess whether the manipulations of IL and TL led to the anticipated effects upon ratings of responsibility/blame, we conducted a 2 (IL condition: low vs. high) 2 (TL condition: low vs. high) ANOVA. A main effect of IL condition emerged, F(1, 147) 6.01, p.02, such that participants assigned to the high IL condition reported that Sam was more responsible for the outcome (M 4.42, SD 2.67) than did participants in the low IL condition (M 3.51, SD 2.12). A main effect of TL condition also emerged, F(1, 147) 4.20, p.05, such that participants assigned to the high TL condition reported that Sam was more responsible for the outcome (M 4.30, SD 2.42) than did participants in the low TL condition (M 3.59, SD 2.43). However, these main effects were qualified by the expected interaction, F(1, 147) 5.74, p.02. Consistent with expectations, when the TL was low, levels of responsibility/blame did not differ with respect to high IL (M 3.60, SD 2.51) and low IL (M 3.58, SD 2.38), t(147) 0.03, ns. However, when TL was high, greater responsibility/ blame was observed when IL was high (M 5.31, SD 2.59) than when it was low (M 3.45, SD 1.88), t(147) 3.42, p.001. To determine whether our experimental manipulations of IL and TL led to the expected effects upon IL and TL ratings (essentially manipulation checks), we conducted separate two-way ANOVAs for each index with the IL and TL conditions as the independent variables. For IL ratings, only a main effect of IL condition was observed, F(1, 147) , p.001, such that participants assigned to the high IL condition reported a greater IL (M 5.45, SD 1.42) than did participants assigned to the low IL condition (M 3.01, SD 1.37). Also as expected, for TL ratings, only a main effect of TL condition was observed, F(1, 147) , p.001, such that participants assigned to the high TL condition reported a greater TL (M 6.63, SD 1.61) than did participants assigned to the low TL condition (M 2.89, SD 1.40). Neither of these main effects was qualified by an interaction (Fs 1). Thus, our manipulations of IL and TL led to the predicted effects upon IL and TL ratings. Finally, to assess whether the IL and TL ratings (which interact as CP) had the predicted interactive effect upon responsibility/ blame, we employed hierarchical regression analyses, following 5 We arrived at this analysis plan after carefully considering an alternative strategy. One argument may be in favor of a Baron and Kenny (1986) approach, whereby we test whether relationships between the manipulated conditions (antecedent and outcome) and the dependent variables are mediated by CP. However, meditational analyses are not appropriate for cases in which the manipulated variable is not conceptually distinct from the mediator (thus, the more effective our manipulations of IL and TL were in influencing IL and TL ratings, the more difficult it would be to find that these ratings mediate other effects). In cases where variables are perfectly manipulated by experimental conditions, the variables are statistically identical to the experimental conditions. Consistent with the arguments of Spencer, Zanna, and Fong (2005), our analytic approach is preferred when the manipulation and the measurement of the proposed process are conceptually the same, as in the current situation.